Is the Group Structure Important in Grouped Functional Time Series?

Yang, Yang; Shang, Han Lin

doi:10.6339/21-JDS1031

Journal of Data Science

Is the Group Structure Important in Grouped Functional Time Series?

Volume 20, Issue 3 (2022): Special Issue: Data Science Meets Social Sciences, pp. 303–324

Yang Yang

Han Lin Shang

https://doi.org/10.6339/21-JDS1031

Pub. online: 4 January 2022 Type: Statistical Data Science

Open Access

Received
30 August 2021

Accepted
8 November 2021

Published
4 January 2022

Abstract

We study the importance of group structure in grouped functional time series. Due to the non-uniqueness of group structure, we investigate different disaggregation structures in grouped functional time series. We address a practical question on whether or not the group structure can affect forecast accuracy. Using a dynamic multivariate functional time series method, we consider joint modeling and forecasting multiple series. Illustrated by Japanese sub-national age-specific mortality rates from 1975 to 2016, we investigate one- to 15-step-ahead point and interval forecast accuracies for the two group structures.

Supplementary material

Supplementary Material

For reproducibility, all R codes are collated in a Github repository at https://github.com/hanshang/GMFTS. This repository contains the following files: • README: Describe the functionality of each R file. • R files with indices 1 to 29: Functions used to compute numerical results presented in the paper. • Example: Contains a quick example of forecasting prefecture-level age-specific mortality rates using the DMFTS method.

References

Aue A, Norinho DD, Hörmann S (2015). On the prediction of stationary functional time series. Journal of the American Statistical Association: Theory and Methods, 110(509): 378–392.

Bali JL, Boente G, Tyler DE, Wang J-L, et al. (2011). Robust functional principal components: A projection-pursuit approach. The Annals of Statistics, 39(6): 2852–2882.

Bassuk SS, Berkman LF, Amick III BC (2002). Socioeconomic status and mortality among the elderly: Findings from four US communities. American Journal of Epidemiology, 155(6): 520–533.

Booth H, Tickle L (2008). Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science, 3(1–2): 3–43.

Cairns AJ, Blake D, Dowd K, Coughlan GD, Khalaf-Allah M M (2011). Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin: The Journal of the IAA, 41(1): 29–59.

Chatfield C (1993). Calculating interval forecasts. Journal of Business & Economic Statistics, 11(2): 121–135.

Chiou J-M (2012). Dynamical functional prediction and classification with application to traffic flow prediction. Annals of Applied Statistics, 6(4): 1588–1614.

Chiou J-M, Chen Y-T, Yang Y-F (2014). Multivariate functional principal component analysis: A normalization approach. Statistica Sinica, 24(4): 1571–1596.

Coulmas F (2007). Population Decline and Ageing in Japan – The Social Consequences. Routledge, New York.

Currie ID, Durban PHC, Eilers M (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4): 279–298.

Dai W, Genton MG (2018). Multivariate functional data visualization and outlier detection. Journal of Computational and Graphical Statistics, 27(4): 923–934.

Dai W, Mrkvička T, Sun Y, Genton MG (2020). Functional outlier detection and taxonomy by sequential transformations. Computational Statistics & Data Analysis, 149: 106960.

Dangerfield BJ, Morris JS (1992). Top-down or bottom-up: Aggregate versus disaggregate extrapolations. International Journal of Forecasting, 8(2): 233–241.

Dowd K, Cairns AJ, Blake D, Coughlan GD, Khalaf-Allah M (2011). A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15(2): 334–356.

Gaille SA, Sherris M (2015). Causes-of-death mortality: What do we know on their dependence? North American Actuarial Journal, 19(2): 116–128.

Gao Y, Shang HL, Yang Y (2019). High-dimensional functional time series forecasting: An application to age-specific mortality rates. Journal of Multivariate Analysis, 170: 232–243.

Gneiting T, Katzfuss M (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 1: 125–151.

Gneiting T, Raftery AE (2007). Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association, 102(477): 359–378.

Hall P, Vial C (2006). Assessing the finite dimensionality of functional data. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 68(4): 689–705.

Happ C, Greven S (2018). Multivariate functional principal component analysis for data observed on different (dimensional) domains. Journal of the American Statistical Association: Theory and Methods, 113(522): 649–659.

Hatzopoulos P, Haberman S (2013). Common mortality modeling and coherent forecasts. an empirical analysis of worldwide mortality data. Insurance. Mathematics & Economics, 52(2): 320–337.

Hyndman RJ, Ahmed RA, Athanasopoulos G, Shang HL (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis, 55(9): 2579–2589.

Hyndman RJ, Shang HL (2009). Forecasting functional time series (with discussions). Journal of the Korean Statistical Society, 38(3): 199–221.

Hyndman RJ, Shang HL (2010). Rainbow plots, bagplots, and boxplots for functional data. Journal of Computational and Graphical Statistics, 19(1): 29–45.

Hyndman RJ, Ullah MS (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics & Data Analysis, 51(10): 4942–4956.

Jacques J, Preda C (2014). Model-based clustering for multivariate functional data. Computational Statistics & Data Analysis, 71: 92–106.

Japanese Mortality Database (2017). National Institute of Population and Social Security Research. Available at http://www.ipss.go.jp/p-toukei/JMD/index-en.html (data downloaded on July 18, 2016).

Jarner SF, Kryger EM (2011). Modelling adult mortality in small populations: The saint model. ASTIN Bulletin: The Journal of the IAA, 41(2): 377–418.

Kolkiewicz A, Rice G, Xie Y (2021). Projection pursuit based tests of normality with functional data. Journal of Statistical Planning and Inference, 211: 326–339.

Murray CJL, Lopez AD (1997). Alternative projections of mortality and disability by cause 1990–2020: Global burden of disease study. The Lancet, 349(9064): 1498–1504.

OECD (2020). Pensions at a glance 2019: OECD and G20 indicators, Technical report, OECD Publishing. Retrieved from http://https://www.oecd-ilibrary.org/social-issues-migration-health/pensions-at-a-glance-2019_b6d3dcfc-en on November 4, 2020.

Perla F, Richman R, Scognamiglio S, Wüthrich MV (2021). Time-series forecasting of mortality rates using deep learning. Scandinavian Actuarial Journal, 2021(7): 572–598.

Rice G, Shang HL (2017). A plug-in bandwidth selection procedure for long-run covariance estimation with stationary functional time series. Journal of Time Series Analysis, 38(4): 591–609.

Rice J, Silverman B (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 53(1): 233–243.

Russolillo M, Giordano G, Haberman S (2011). Extending the Lee–Carter model: A three-way decomposition. Scandinavian Actuarial Journal, 2011(2): 96–117.

Sefton J, Weale M (2009). Reconciliation of National Income and Expenditure: Balanced Estimates of National Income for the United Kingdom 1920–1990. Cambridge University Press, Cambridge.

Shang HL (2016). Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method. Annals of Applied Statistics, 10(3): 1639–1672.

Shang HL (2017). Reconciling forecasts of infant mortality rates at national and sub-national levels: Grouped time-series methods. Population Research and Policy Review, 36(1): 55–84.

Shang HL (2018). Bootstrap methods for stationary functional time series. Statistics and Computing, 28(1): 1–10.

Shang HL (2019). Dynamic principal component regression: Application to age-specific mortality forecasting. ASTIN Bulletin: The Journal of the IAA, 49(3): 619–645.

Shang HL, Hyndman RJ (2017). Grouped functional time series forecasting: An application to age-specific mortality rates. Journal of Computational and Graphical Statistics, 26(2): 330–343.

Shang HL, Kearney F (2021). Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces. International Journal of Forecasting. In press.

Shang HL, Yang Y, Kearney F (2019). Intraday forecasts of a volatility index: Functional time series methods with dynamic updating. Annals of Operations Research, 282(1): 331–354.

Singh GK, Azuine RE, Siahpush M, Kogan MD (2013). All-cause and cause-specific mortality among US youth: Socioeconomic and rural-urban disparities and international patterns. Journal of Urban Health, 90(3): 388–405.

Singh GK, Siahpush M (2001). All-cause and cause-specific mortality of immigrants and native born in the United States. American Journal of Public Health, 91(3): 392.

Stone R, Champernowne DG, Meade JE (1942). The precision of national income estimates. The Review of Economic Studies, 9(2): 111–125.

The Government of Japan (2021). Japan’s Regional Strength. Available at https://www.japan.go.jp/regions/index.html (Accessed August 26, 2021).

Villegas AM, Haberman S, Kaishev VK, Millossovich P (2017). A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin: The Journal of the IAA, 47(3): 631–679.

Wickramasuriya SL, Athanasopoulos G, Hyndman RJ (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association: Theory and Methods, 114(526): 804–819.

Wood SN (2003). Thin plate regression splines. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 65(1): 95–114.

Yao F, Müller H-G, Wang J-L (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association: Theory and Methods, 100(470): 577–590.

Zellner A, Tobias J (2000). A note on aggregation, disaggregation and forecasting performance. Journal of Forecasting, 19(5): 457–465.

Zhang L, Shen H, Huang JZ (2013). Robust regularized singular value decomposition with application to mortality data. Annals of Applied Statistics, 7(3): 1540–1561.

Zivot E, Wang J (2006). Modeling Financial Time Series with S-PLUS. Springer, New York.

2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

dynamic principal component analysis forecast reconciliation Japanese sub-national age-specific mortality rates long-run covariance function multivariate functional principal component analysis

Metrics

since February 2021

1426 Article info views	0 Full article views
469 PDF downloads	300 XML downloads

RSS

Authors

Abstract

Supplementary material

References

Export citation

Copy and paste formatted citation

Download citation in file